Traditionally, the “speed” of an optical design is dictated by the aberrations that can be tolerated for a given complexity of the design. Aberrations reduce the image forming capacity of optical systems. An optical design may avoid or reduce aberrations by sacrificing size, cost, light collection, and possibly other performance criteria.
Computational imaging (“CI”) techniques may be used to circumvent the traditional design limitations through aberration compensation performed in signal post-processing. To restore image quality, CI techniques may exploit knowledge of the optical transfer function (“OTF”) of the design, to create filters that compensate for the known aberrations in the design.
Wiener filtering may use the known optical transfer function and noise statistics to produce a linear transfer function that, when multiplied by the OTF, reduces the error in the resulting product. While it may be optimal in the sense of producing the least square error (“LSE”), Wiener filtering and other techniques are fundamentally limited in their correction ability by the optical information lost in the imaging system (i.e., the optical information lost between the imaged object and a corrupted image of the object formed by the system on the image capturing element of the system, such as image sensor). While the magnitude of the optical transfer function (“MTF”) approaches zero at the cutoff spatial frequency, the loss of additional information (i.e., the presence of MTF zeros or greatly reduced values, such as values reduced by 10 dB, 20 dB, or 30 dB below peak of the MTF) at much lower spatial frequencies is associated with aberrations. Thus, imaging techniques are limited by the presence in the OTF of zeroes or relatively low values, such as values below a detectable limit.